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Longer titles found: Holomorphic functional calculus (view), Antiholomorphic function (view), Formal holomorphic function (view), Milne-Thomson method for finding a holomorphic function (view), Analyticity of holomorphic functions (view)

searching for Holomorphic function 36 found (216 total)

alternate case: holomorphic function

Cartan's theorems A and B (352 words) [view diff] exact match in snippet view article find links to article

they imply that a holomorphic function on a closed complex submanifold, Z, of a Stein manifold X can be extended to a holomorphic function on all of X. At
List of zeta functions (354 words) [view diff] exact match in snippet view article find links to article
interval of a poset to the constant value 1. Despite not resembling a holomorphic function, the special case for the poset of integer divisibility is related
Prime form (198 words) [view diff] exact match in snippet view article find links to article
and vanishes if and only if x = y. The prime form E is not quite a holomorphic function on X × X, but is a section of a holomorphic line bundle over this
Schottky's theorem (321 words) [view diff] exact match in snippet view article find links to article
quantitative version of Picard's theorem. It states that that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, the
Schottky's theorem (321 words) [view diff] exact match in snippet view article find links to article
quantitative version of Picard's theorem. It states that that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, the
Modular lambda function (1,226 words) [view diff] exact match in snippet view article find links to article
the elliptic modular lambda function λ(τ) is a highly symmetric holomorphic function on the complex upper half-plane. It is invariant under the fractional
George Adam Pfeiffer (555 words) [view diff] exact match in snippet view article find links to article
in 1943. Pfeiffer is known for publishing the first example of a holomorphic function with a non-linearizable irrational indifferent fixed point. The question
Adjunction formula (1,781 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\mathcal {O}}(D)} can be written as s/f, where s is a holomorphic function on U. Let η be a section over U of ωX. The Poincaré residue is the
Paley–Wiener theorem (1,234 words) [view diff] exact match in snippet view article find links to article
_{0}^{\infty }F(x)e^{ix\zeta }\,dx} for ζ in the upper half-plane is a holomorphic function. Moreover, by Plancherel's theorem, one has ∫ − ∞ ∞ | f ( ξ + i η
Dirichlet density (593 words) [view diff] exact match in snippet view article find links to article
pole as it has non-integral order), at least if this function is a holomorphic function times a (real) power of s−1 near s = 1. For example, if A is the
Eisenstein series (3,180 words) [view diff] exact match in snippet view article find links to article
converges to a holomorphic function of τ in the upper half-plane and its Fourier expansion given below shows that it extends to a holomorphic function at τ =
List of mathematical functions (1,061 words) [view diff] exact match in snippet view article find links to article
of the prime p Modular lambda function, λ(τ), a highly symmetric holomorphic function on the complex upper half-plane Lamé function Mathieu function Mittag-Leffler
Singular integral operators on closed curves (4,933 words) [view diff] exact match in snippet view article find links to article
proved, in a result that was a precursor of Mergelyan's theorem, any holomorphic function on Ω that extends continuously to the closure can be approximated
Appell–Humbert theorem (471 words) [view diff] exact match in snippet view article find links to article
functions on V, and for each u the expression above is a corresponding holomorphic function. The Appell–Humbert theorem (Mumford 2008) says that every line bundle
Metaplectic group (1,391 words) [view diff] exact match in snippet view article find links to article
{\displaystyle g\in \mathrm {SL} _{2}(\mathbf {R} )} and ε is a holomorphic function on the upper half-plane such that ϵ ( z ) 2 = c z + d = j ( g , z
Glossary of functional analysis (2,606 words) [view diff] exact match in snippet view article find links to article
states: if x is an element of a unital Banach algebra and f is a holomorphic function in a neighborhood of the spectrum σ ( x ) {\displaystyle \sigma (x)}
Seiberg–Witten theory (834 words) [view diff] exact match in snippet view article find links to article
four-fermions low-energy action can be expressed in terms of a single holomorphic function F {\displaystyle {\mathcal {F}}} , as follows: The first term is
Bandlimiting (942 words) [view diff] exact match in snippet view article find links to article
theorem in complex analysis that says that all zeros of non-constant holomorphic function are isolated. But this contradicts our earlier finding that F 2 {\displaystyle
Unified field theory (1,868 words) [view diff] exact match in snippet view article find links to article
Y + {\displaystyle Y^{+}} manifold. In mathematics, if f(z) is a holomorphic function restricted to the Real Numbers, it has the complex conjugate properties
Denjoy–Wolff theorem (965 words) [view diff] exact match in snippet view article find links to article
Wolff. Theorem. Let D be the open unit disk in C and let f be a holomorphic function mapping D into D which is not an automorphism of D (i.e. a Möbius
Conformal welding (1,123 words) [view diff] exact match in snippet view article find links to article
have smooth boundary values on the circle related by f. Since the holomorphic function on Dc vanishes at ∞, the positive powers of this pair also provide
Hilbert's Nullstellensatz (2,714 words) [view diff] exact match in snippet view article find links to article
{\mathcal {O}}_{\mathbb {C} ^{n},0}} is a germ represented by a holomorphic function f ~ : U → C {\displaystyle {\widetilde {f}}:U\to \mathbb {C} } ,
Analytic number theory (3,518 words) [view diff] exact match in snippet view article find links to article
many cases, even where the series does not converge everywhere, the holomorphic function it defines may be analytically continued to a meromorphic function
Donald Sarason (1,205 words) [view diff] exact match in snippet view article find links to article
theorem of G. Pick on when an interpolation problem can be solved by a holomorphic function that maps the disk to itself; this is often called Nevanlinna-Pick
D-module (2,064 words) [view diff] exact match in snippet view article find links to article
solutions of the differential equation P f = 0, where f is some holomorphic function in C, say. The vector space consisting of the solutions of that equation
Neumann–Poincaré operator (11,008 words) [view diff] exact match in snippet view article find links to article
=\,\,\int _{|z|=R}\partial _{n}u.}} At ∞ u is the real part of a holomorphic function F with F ( z ) = a 0 + a 1 z − 1 + a 2 z − 2 + ⋯ {\displaystyle \displaystyle
Differential forms on a Riemann surface (11,032 words) [view diff] exact match in snippet view article find links to article
1-forms locally have the form df with f a holomorphic function and since the real part of a holomorphic function is harmonic, harmonic 1-forms locally have
Hodge star operator (5,108 words) [view diff] exact match in snippet view article find links to article
invariant under holomorphic changes of coordinate. If z = x + iy is a holomorphic function of w = u + iv, then by the Cauchy–Riemann equations we have that
Series (mathematics) (8,592 words) [view diff] exact match in snippet view article
absolutely when Re s > 1, but the zeta function can be extended to a holomorphic function defined on C ∖ { 1 } {\displaystyle \mathbf {C} \setminus \{1\}}
Hypergeometric function (7,016 words) [view diff] exact match in snippet view article find links to article
there are usually two special solutions of the form xs times a holomorphic function of x, where s is one of the two roots of the indicial equation and
Wigner quasiprobability distribution (4,602 words) [view diff] exact match in snippet view article find links to article
) = e g ( x + i p ) {\displaystyle F(x+ip)=e^{g(x+ip)}} for some holomorphic function g {\displaystyle g} . But in order for F {\displaystyle F} to belong
Moduli stack of elliptic curves (2,346 words) [view diff] exact match in snippet view article find links to article
\right)=(c\tau +d)^{k}f(\tau )} This is exactly the condition for a holomorphic function to be modular. The modular forms are the modular functions which
Knizhnik–Zamolodchikov equations (2,968 words) [view diff] exact match in snippet view article find links to article
correlation function can be analytically continued as multi-valued holomorphic function to the domain X n ⊂ C n {\displaystyle X_{n}\subset \mathbb {C} ^{n}}
Generalized conic (2,764 words) [view diff] exact match in snippet view article find links to article
in the theory of approximation. The polynomial approximation of a holomorphic function can be interpreted as the approximation of the level curves with
Planar Riemann surface (3,689 words) [view diff] exact match in snippet view article find links to article
Let X be a Riemann surface and W an open connected subset with a holomorphic function g = u + iv differing from f by a constant such that g(W) lies in
Singular integral operators of convolution type (12,875 words) [view diff] exact match in snippet view article find links to article
on H in the following sense: f is in H2 provided that there is a holomorphic function F(z) on H such that the functions fy(x) = f(x + iy) for y > 0 are